Lawrence of Puzzlania

 While crossing the Puzzlanian desert, you become lost in a sandstorm. After wandering for days, your water supply nearly exhausted, you come upon an oasis. With plenty of fresh water and edible flora about, you replenish your supplies and contemplate your situation.

You know from experience that you can carry about three days worth of water and food. Your most efficient walking pace covers about twenty miles in a day. You have an accurate compass, so you can travel in a straight line, but you don't know where you are. Fortunately, you know that no part of the desert is more than a hundred miles in any direction from civilization.

Two questions:

1. How quickly can you guarantee escape from the desert?
2. If the desert was more than a hundred miles in radius, what's the furthest you could travel given unlimited time?

Assume that the oasis has unlimited supplies, you can always find any supplies you drop along the way, and that you can drop water and food in arbitrary amounts.